Mathematics, 26.02.2021 18:50 theatergeek005
Which statement completes step 6 of the proof?
Coordinate plane with line f at y equals 3 times x plus 1 and line g at y equals negative one third times x plus 1. Triangle JKL is at J negative 1 comma negative 2, K 0 comma 1, and L 0 comma negative 2. Triangle J prime K L prime is at J prime negative 3 comma 2, K 0 comma 1, and L prime negative 3 comma 1.
Step 1 segment KL is parallel to the y-axis, and segment JL is parallel to the x-axis.
Step 2 ΔJKL was rotated 90° clockwise to create ΔJ'KL'. Point K did not change position, so it remains point K. Therefore, ΔJKL ≅ ΔJ'KL'.
Step 3 segment K L prime is perpendicular to the y-axis, and segment J prime L prime is perpendicular to the x-axis.
Step 4 segment JK lies on line f and has a slope of 3.
Step 5 segment J prime K lies on line g and has a slope of negative one third.
Step 6 ?
The product of the slopes of segment JK and segment J prime K is −1; therefore, lines f and g are perpendicular.
The slopes of segment JK and segment J prime K are congruent; therefore, lines f and g are parallel.
The product of the slopes of segment KL and segment K L prime is −1; therefore, lines f and g are perpendicular.
The slopes of segment KL and segment K L prime are congruent; therefore, lines f and g are parallel.
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Which statement completes step 6 of the proof?
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